Ocular optical system

ABSTRACT

An ocular optical system includes a first lens element and a second lens element from an eye-side to a display-side in order along an optical axis. The first lens element and the second lens element each include an eye-side surface and a display-side surface. The eye-side surface of the first lens element has a convex portion in a vicinity of the optical axis. The second lens element has negative refracting power. The ocular optical system satisfies 1.5≤|f2/f1| and 250 millimeters/EFL≤10, wherein f2 is the focal length of the second lens element, f1 is the focal length of the first lens element, and EFL is the effective focal length of the ocular optical system.

CROSS-REFERENCE TO RELATED APPLICATION

This application is a continuation application of and claims thepriority benefit of U.S. application Ser. No. 15/348,904, filed on Nov.10, 2016, now allowed, which claims the priority benefit of Chinaapplication serial no. 201610862363.5, filed on Sep. 29, 2016. Theentirety of each of the above-mentioned patent applications is herebyincorporated by reference herein and made a part of this specification.

BACKGROUND OF THE INVENTION 1. Field of the Invention

The invention relates to an optical system, and particularly, to anocular optical system.

2. Description of Related Art

Virtual Reality (VR) refers to computer technologies used for simulatingand generating a three-dimensional virtual world, which enablesimmersive simulation for users by providing simulations pertaining tovisual sensation, auditory sensation and other sensations to users. Thecurrently existing VR devices are mainly focused on visual experiences.Binocular parallax of human eyes is simulated by separated images withtwo slightly different perspectives corresponding to the left and righteyes to achieve a stereo vision. In order to reduce the volume of the VRdevice so users can receive a magnified visual sensation from a smallerdisplay screen, an ocular optical system with magnifying capability isnow one of major topics in research and development for VR.

Because a half apparent field of view is smaller in the existing ocularoptical system, an observer may experience narrow vision, low resolutionand even aberrations so serious that an aberration compensation must beperformed on the display screen before presentation. Accordingly, how toincrease the half apparent field of view and enhance the imaging qualitybecomes one of issues to be addressed.

SUMMARY OF THE INVENTION

The invention is directed to an ocular optical system, which is capableof shortening a system length without sacrificing a favorable imagingquality and a large half apparent field of view.

An embodiment of the invention proposes an ocular optical system forimaging of imaging rays entering an eye of an observer via the ocularoptical system from a display screen, where a side facing towards theeye is an eye-side and a side facing towards the display screen is adisplay-side. The ocular optical system includes a first lens elementand a second lens element from the eye-side to the display-side in orderalong an optical axis. The first lens element and the second lenselement each include an eye-side surface and a display-side surface.

The eye-side surface of the first lens element has a convex portion in avicinity of the optical axis. The second lens element has negativerefracting power. The ocular optical system satisfies 1.5≤|f2/f1| and250 millimeters/EFL≤10, wherein f2 is a focal length of the second lenselement, f1 is a focal length of the first lens element, and EFL is aneffective focal length of the ocular optical system.

Based on the above, in the embodiments of the invention, the ocularoptical system can provide the following advantageous effects. Withdesign and arrangement of the lens elements in terms of surface shapesand refracting powers as well as design of optical parameters, theocular optical system can include optical properties for overcoming theaberrations and provide the favorable imaging quality and the largeapparent field of view, given that the system length is shorten.

To make the above features and advantages of the invention morecomprehensible, several embodiments accompanied with drawings aredescribed in detail as follows.

BRIEF DESCRIPTION OF THE DRAWINGS

The accompanying drawings are included to provide a furtherunderstanding of the invention, and are incorporated in and constitute apart of this specification. The drawings illustrate embodiments of theinvention and, together with the description, serve to explain theprinciples of the invention.

FIG. 1 is a schematic view illustrating an ocular optical system.

FIG. 2 is a schematic view illustrating a surface structure of a lenselement.

FIG. 3 is a schematic view illustrating a concave and convex surfacestructure of a lens element and a ray focal point.

FIG. 4 is a schematic view illustrating a surface structure of a lenselement according to a first example.

FIG. 5 is a schematic view illustrating a surface structure of a lenselement according to a second example.

FIG. 6 is a schematic view illustrating a surface structure of a lenselement according to a third example.

FIG. 7 is a schematic view illustrating an ocular optical systemaccording to a first embodiment of the invention.

FIG. 8A to FIG. 8D illustrate a longitudinal spherical aberration andother aberrations of the ocular optical system according to the firstembodiment of the invention.

FIG. 9 shows detailed optical data pertaining to the ocular opticalsystem according to the first embodiment of the invention.

FIG. 10 shows aspheric parameters pertaining to the ocular opticalsystem according to the first embodiment of the invention.

FIG. 11 is a schematic view illustrating an ocular optical systemaccording to a second embodiment of the invention.

FIG. 12A to FIG. 12D illustrate a longitudinal spherical aberration andother aberrations of the ocular optical system according to the secondembodiment of the invention.

FIG. 13 shows detailed optical data pertaining to the ocular opticalsystem according to the second embodiment of the invention.

FIG. 14 shows aspheric parameters pertaining to the ocular opticalsystem according to the second embodiment of the invention.

FIG. 15 is a schematic view illustrating an ocular optical systemaccording to a third embodiment of the invention.

FIG. 16A to FIG. 16D illustrate a longitudinal spherical aberration andother aberrations of the ocular optical system according to the thirdembodiment of the invention.

FIG. 17 shows detailed optical data pertaining to the ocular opticalsystem according to the third embodiment of the invention.

FIG. 18 shows aspheric parameters pertaining to the ocular opticalsystem according to the third embodiment of the invention.

FIG. 19 is a schematic view illustrating an ocular optical systemaccording to a fourth embodiment of the invention.

FIG. 20A to FIG. 20D illustrate a longitudinal spherical aberration andother aberrations of the ocular optical system according to the fourthembodiment of the invention.

FIG. 21 shows detailed optical data pertaining to the ocular opticalsystem according to the fourth embodiment of the invention.

FIG. 22 shows aspheric parameters pertaining to the ocular opticalsystem according to the fourth embodiment of the invention.

FIG. 23 is a schematic view illustrating an ocular optical systemaccording to a fifth embodiment of the invention.

FIG. 24A to FIG. 24D illustrate a longitudinal spherical aberration andother aberrations of the ocular optical system according to the fifthembodiment of the invention.

FIG. 25 shows detailed optical data pertaining to the ocular opticalsystem according to the fifth embodiment of the invention.

FIG. 26 shows aspheric parameters pertaining to the ocular opticalsystem according to the fifth embodiment of the invention.

FIG. 27 is a schematic view illustrating an ocular optical systemaccording to a sixth embodiment of the invention.

FIG. 28A to FIG. 28D illustrate a longitudinal spherical aberration andother aberrations of the ocular optical system according to the sixthembodiment of the invention.

FIG. 29 shows detailed optical data pertaining to the ocular opticalsystem according to the sixth embodiment of the invention.

FIG. 30 shows aspheric parameters pertaining to the ocular opticalsystem according to the sixth embodiment of the invention.

FIG. 31 is a schematic view illustrating an ocular optical systemaccording to a seventh embodiment of the invention.

FIG. 32A to FIG. 32D illustrate a longitudinal spherical aberration andother aberrations of the ocular optical system according to the seventhembodiment of the invention.

FIG. 33 shows detailed optical data pertaining to the ocular opticalsystem according to the seventh embodiment of the invention.

FIG. 34 shows aspheric parameters pertaining to the ocular opticalsystem according to the seventh embodiment of the invention.

FIG. 35 is a schematic view illustrating an ocular optical systemaccording to an eighth embodiment of the invention.

FIG. 36A to FIG. 36D illustrate a longitudinal spherical aberration andother aberrations of the ocular optical system according to the eighthembodiment of the invention.

FIG. 37 shows detailed optical data pertaining to the ocular opticalsystem according to the eighth embodiment of the invention.

FIG. 38 shows aspheric parameters pertaining to the ocular opticalsystem according to the eighth embodiment of the invention.

FIG. 39 is a schematic view illustrating an ocular optical systemaccording to a ninth embodiment of the invention.

FIG. 40A to FIG. 40D illustrate a longitudinal spherical aberration andother aberrations of the ocular optical system according to the ninthembodiment of the invention.

FIG. 41 shows detailed optical data pertaining to the ocular opticalsystem according to the ninth embodiment of the invention.

FIG. 42 shows aspheric parameters pertaining to the ocular opticalsystem according to the ninth embodiment of the invention.

FIG. 43 and FIG. 44 show important parameters and relation valuesthereof pertaining to the ocular optical system according to the firstthrough the ninth embodiments of the invention.

DESCRIPTION OF THE EMBODIMENTS

Reference will now be made in detail to the present preferredembodiments of the invention, examples of which are illustrated in theaccompanying drawings. Wherever possible, the same reference numbers areused in the drawings and the description to refer to the same or likeparts.

In general, a ray direction of an ocular optical system V100 refers tothe following: imaging rays VI are emitted by a display screen V50,enter an eye V60 via the ocular optical system V100, and are thenfocused on a retina of the eye V60 for imaging and generating anenlarged virtual image VV at a least distance of distinct vision VD, asdepicted in FIG. 1. The following criteria for determining opticalspecifications of the present application are based on assumption that areversely tracking of the ray direction is parallel imaging rays passingthrough the ocular optical system from an eye-side and focused on thedisplay screen for imaging.

In the present specification, the description “a lens element havingpositive refracting power (or negative refracting power)” means that theparaxial refracting power of the lens element in Gaussian optics ispositive (or negative). The description “An eye-side (or display-side)surface of a lens element” only includes a specific region of thatsurface of the lens element where imaging rays are capable of passingthrough that region, namely the clear aperture of the surface. Theaforementioned imaging rays can be classified into two types, chief rayLc and marginal ray Lm. Taking a lens element depicted in FIG. 2 as anexample, I is an optical axis and the lens element is rotationallysymmetric, where the optical axis I is the axis of symmetry. The regionA of the lens element is defined as “a portion in a vicinity of theoptical axis”, and the region C of the lens element is defined as “aportion in a vicinity of a periphery of the lens element”. Besides, thelens element may also have an extending portion E extended radially andoutwardly from the region C, namely the portion outside of the clearaperture of the lens element. The extending portion E is usually usedfor physically assembling the lens element into an optical imaging lenssystem. Under normal circumstances, the imaging rays would not passthrough the extending portion E because those imaging rays only passthrough the clear aperture. The structures and shapes of theaforementioned extending portion E are only examples for technicalexplanation, the structures and shapes of lens elements should not belimited to these examples. Note that the extending portions of the lenselement surfaces depicted in the following embodiments are partiallyomitted.

The following criteria are provided for determining the shapes and theportions of lens element surfaces set forth in the presentspecification. These criteria mainly determine the boundaries ofportions under various circumstances including the portion in a vicinityof the optical axis, the portion in a vicinity of a periphery of a lenselement surface, and other types of lens element surfaces such as thosehaving multiple portions.

1. FIG. 2 is a radial cross-sectional view of a lens element. Beforedetermining boundaries of those aforesaid portions, two referentialpoints should be defined first, central point and transition point. Thecentral point of a surface of a lens element is a point of intersectionof that surface and the optical axis. The transition point is a point ona surface of a lens element, where the tangent line of that point isperpendicular to the optical axis. Additionally, if multiple transitionpoints appear on one single surface, then these transition points aresequentially named along the radial direction of the surface withnumbers starting from the first transition point. For instance, thefirst transition point (closest one to the optical axis), the secondtransition point, and the Nth transition point (farthest one to theoptical axis within the scope of the clear aperture of the surface). Theportion of a surface of the lens element between the central point andthe first transition point is defined as the portion in a vicinity ofthe optical axis. The portion located radially outside of the Nthtransition point (but still within the scope of the clear aperture) isdefined as the portion in a vicinity of a periphery of the lens element.In some embodiments, there are other portions existing between theportion in a vicinity of the optical axis and the portion in a vicinityof a periphery of the lens element; the numbers of portions depend onthe numbers of the transition point(s). In addition, the radius of theclear aperture (or a so-called effective radius) of a surface is definedas the radial distance from the optical axis I to a point ofintersection of the marginal ray Lm and the surface of the lens element.

2. Referring to FIG. 3, determining the shape of a portion is convex orconcave depends on whether a collimated ray passing through that portionconverges or diverges. That is, while applying a collimated ray to aportion to be determined in terms of shape, the collimated ray passingthrough that portion will be bended and the ray itself or its extensionline will eventually meet the optical axis. The shape of that portioncan be determined by whether the ray or its extension line meets(intersects) the optical axis (focal point) at the eye-side ordisplay-side. For instance, if the ray itself intersects the opticalaxis at the display-side of the lens element after passing through aportion, i.e. the focal point of this ray is at the display-side (seepoint R in FIG. 3), the portion will be determined as having a convexshape. On the contrary, if the ray diverges after passing through aportion, the extension line of the ray intersects the optical axis atthe eye-side of the lens element, i.e. the focal point of the ray is atthe eye-side (see point M in FIG. 3), that portion will be determined ashaving a concave shape. Therefore, referring to FIG. 3, the portionbetween the central point and the first transition point has a convexshape, the portion located radially outside of the first transitionpoint has a concave shape, and the first transition point is the pointwhere the portion having a convex shape changes to the portion having aconcave shape, namely the border of two adjacent portions.Alternatively, there is another common way for a person with ordinaryskill in the art to tell whether a portion in a vicinity of the opticalaxis has a convex or concave shape by referring to the sign of an “R”value, which is the (paraxial) radius of curvature of a lens surface.The R value which is commonly used in conventional optical designsoftware such as Zemax and CodeV. The R value usually appears in thelens data sheet in the software. For an eye-side surface, positive Rmeans that the eye-side surface is convex, and negative R means that theeye-side surface is concave. Conversely, for a display-side surface,positive R means that the display-side surface is concave, and negativeR means that the display-side surface is convex. The result found byusing this method should be consistent as by using the other waymentioned above, which determines surface shapes by referring to whetherthe focal point of a collimated ray is at the eye-side or thedisplay-side.

3. For none transition point cases, the portion in a vicinity of theoptical axis is defined as the portion between 0-50% of the effectiveradius (radius of the clear aperture) of the surface, whereas theportion in a vicinity of a periphery of the lens element is defined asthe portion between 50-100% of effective radius (radius of the clearaperture) of the surface.

Referring to the first example depicted in FIG. 4, only one transitionpoint, namely a first transition point, appears within the clearaperture of the display-side surface of the lens element. Portion I is aportion in a vicinity of the optical axis, and portion II is a portionin a vicinity of a periphery of the lens element. The portion in avicinity of the optical axis is determined as having a concave surfacedue to the R value at the display-side surface of the lens element ispositive. The shape of the portion in a vicinity of a periphery of thelens element is different from that of the radially inner adjacentportion, i.e. the shape of the portion in a vicinity of a periphery ofthe lens element is different from the shape of the portion in avicinity of the optical axis; the portion in a vicinity of a peripheryof the lens element has a convex shape.

Referring to the second example depicted in FIG. 5, a first transitionpoint and a second transition point exist on the eye-side surface(within the clear aperture) of a lens element. In which portion I is theportion in a vicinity of the optical axis, and portion III is theportion in a vicinity of a periphery of the lens element. The portion ina vicinity of the optical axis has a convex shape because the R value atthe eye-side surface of the lens element is positive. The portion in avicinity of a periphery of the lens element (portion III) has a convexshape. What is more, there is another portion having a concave shapeexisting between the first and second transition point (portion II).

Referring to a third example depicted in FIG. 6, no transition pointexists on the eye-side surface of the lens element. In this case, theportion between 0-50% of the effective radius (radius of the clearaperture) is determined as the portion in a vicinity of the opticalaxis, and the portion between 50-100% of the effective radius isdetermined as the portion in a vicinity of a periphery of the lenselement. The portion in a vicinity of the optical axis of the eye-sidesurface of the lens element is determined as having a convex shape dueto its positive R value, and the portion in a vicinity of a periphery ofthe lens element is determined as having a convex shape as well.

FIG. 7 is a schematic view illustrating an ocular optical systemaccording to the first embodiment of the invention, and FIG. 8A to FIG.8D illustrate a longitudinal spherical aberration and other aberrationsof the ocular optical system according to the first embodiment of theinvention. Referring to FIG. 7, an ocular optical system 10 according tothe first embodiment of the invention is used for imaging of imagingrays entering an eye of an observer via the ocular optical system 10 anda pupil 2 of the eye of the observer from a display screen 100. A sidefacing towards the eye is an eye-side, a side facing towards the displayscreen 100 is a display-side. The ocular optical system 10 includes afirst lens element 3 and a second lens element 4 from the eye-side tothe display-side in order along an optical axis I of the ocular opticalsystem 10. When the rays emitted by the display screen 100 enter theocular optical system 10, pass through the second lens elements 4 andthe first lens element 3 in order, and enter the eye of the observer viathe pupil 2, an image is formed on a retina of the eye.

The first lens element 3 and the second lens element 4 each include aneye-side surface 31, 41 facing the eye-side and allowing the imagingrays to pass through and a display-side surface 32, 42 facing thedisplay-side and allowing the imaging rays to pass through. In order tomeet the demand for lighter products, the first lens element 3 and thesecond lens element 4 all have refracting power. Besides, the first lenselement 3 and the second lens element 4 are made of plastic material;nevertheless, the material of the first lens element 3 and the secondlens element 4 is not limited thereto.

The first lens element 3 has positive refracting power. The eye-sidesurface 31 of the first lens element 3 is a convex surface, and has aconvex portion 311 in a vicinity of the optical axis I and a convexportion 313 in a vicinity of a periphery of the first lens element 3.The display-side surface 32 of the first lens element 3 is a convexsurface, and has a convex portion 321 in a vicinity of the optical axisI and a convex portion 323 in a vicinity of a periphery of the firstlens element 3.

The second lens element 4 has negative refracting power. The eye-sidesurface 41 of the second lens element 4 has a convex portion 411 in avicinity of the optical axis I and a concave portion 414 in a vicinityof a periphery of the second lens element 4. The display-side surface 42of the second lens element 4 is a concave surface, and has a concaveportion 422 in a vicinity of the optical axis I and a concave portion424 in a vicinity of a periphery of the second lens element 4.

Further, in the present embodiment, only the aforesaid lens elementshave refracting power, and the ocular optical system 10 includes onlythe two lens elements having the refracting power. One of the eye-sidesurface 31 and the display-side surface 32 of the first lens element 3and the eye-side surface 41 and the display-side surface 42 of thesecond lens element 4 is a Fresnel surface, which is a surface of aFresnel lens. In the present embodiment, the display-side surface 32 ofthe first lens element 3 is the Fresnel surface 33.

In addition, the relationship among the important parameters pertainingto the ocular optical system 10 in the first embodiment is indicated inFIG. 1 and FIG. 43. wherein

EPD represents an exit pupil diameter of the ocular optical system 10corresponding to a diameter of the pupil 2 of the observer, which isapproximately 3 mm during the day and approximately 7 mm at night, asdepicted in FIG. 1;

ER (eye relief) represents an exit pupil distance, which is a distancefrom the pupil 2 of the observer to the first lens element 3 along theoptical axis I;

ω represents a half apparent field of view, which is one half the fieldof view of the observer, as depicted in FIG. 1;

T1 represents a thickness of the first lens element 3 along the opticalaxis I;

T2 represents a thickness of the second lens element 4 along the opticalaxis I;

G12 represents a distance from the display-side surface 32 of the firstlens element 3 to the eye-side surface 41 of the second lens element 4along the optical axis I, which is an air gap from the first lenselement 3 to the second lens element 4 along the optical axis I;

G2D represents a distance from the display-side surface 42 of the secondlens element 4 to the display screen 100 along the optical axis I, whichis an air gap from the second lens element 4 to the display screen 100along the optical axis I;

DLD represents a diagonal length of the display screen 100 correspondingto one single pupil 2 of the observer, as depicted in FIG. 1;

a least distance of distinct vision is the closest distance that the eyeis able to clearly focus on, which is normally 250 millimeters (mm) foryoung people, i.e., the least distance of distinct vision VD depicted inFIG. 1;

ALT represents a sum of the thicknesses of the first lens element 3 andthe second lens element 4 along the optical axis I, i.e., a sum of T1and T2;

TTL represents a distance from the eye-side surface 31 of the first lenselement 3 to the display screen 100 along the optical axis I;

TL represents a distance from the eye-side surface 31 of the first lenselement 3 to the display-side surface 42 of the second lens element 4along the optical axis I;

SL represents a system length, which is a distance from the pupil 2 ofthe observer to the display screen 100 along the optical axis I; and

EFL represents an effective focal length of the ocular optical system10.

Besides, it is further defined that:

f1 is a focal length of the first lens element 3;

f2 is a focal length of the second lens element 4;

n1 is a refractive index of the first lens element 3;

n2 is a refractive index of the second lens element 4;

v1 is an Abbe number of the first lens element 3, and the Abbe number isalso known as a dispersion coefficient;

v2 is an Abbe number of the second lens element 4;

D1 is the diameter of the clear aperture of the eye-side surface 31 ofthe first lens element 3; and

D2 is the diameter of the clear aperture of the eye-side surface 41 ofthe second lens element 4.

Other detailed optical data in the first embodiment are indicated inFIG. 9. In the first embodiment, the effective focal length (EFL) (i.e.system focal length) of the ocular optical system 10 is 40.562 mm, thehalf apparent field of view (ω) thereof is 44.999°, TTL thereof is47.198 mm, EPD thereof is 2.000 mm, 0.5 times DLD thereof is 33.262 mm,and SL thereof is 62.198 mm. Among them, the effective radius in FIG. 9refers to one half the diameter of the clear aperture.

Further, in the present embodiment, the eye-side surface 31 of the firstlens element 3 and the eye-side surface 41 and the display-side surface42 of the second lens element 4 (three surfaces in total) are theaspheric surfaces, whereas the display-side surface 32 of the first lenselement 3 is the Fresnel surface 33, wherein an arc surface of eachtooth of the Fresnel surface 33 (i.e., a curved surface on each toothfor effectively refracting the imaging rays) is an aspheric surface, andthe following aspheric coefficients of the display-side surface 32 areused to represent the arc surfaces of the teeth. The aspheric surfacesare defined by the following formula.

$\begin{matrix}{{Z(Y)} = {{\frac{Y^{2}}{R}\text{/}\left( {1 + \sqrt{1 - {\left( {1 + K} \right)\frac{Y^{2}}{R^{2}}}}} \right)} + {\sum\limits_{i = 1}^{n}\; {a_{i} \times Y^{i}}}}} & (1)\end{matrix}$

wherein

Y: a distance from a point on an aspheric curve to the optical axis I;

Z: a depth of the aspheric surface (a vertical distance between thepoint on the aspheric surface that is spaced from the optical axis I bythe distance Y and a tangent plane tangent to a vertex of the asphericsurface on the optical axis I);

R: a radius of curvature of the surface of the lens element close to theoptical axis I;

K: a conic constant;

α_(i): the i^(th) aspheric coefficient.

The aspheric coefficients of the eye-side surfaces 31 and 41 and thedisplay-side surfaces 32 and 42 in the formula (1) are indicated in FIG.10. In FIG. 10, the referential number 31 is one row that represents theaspheric coefficient of the eye-side surface 31 of the first lenselement 3, and the reference numbers in other rows can be deduced fromthe above.

Referring to FIG. 8A to FIG. 8D, FIG. 8A to FIG. 8D illustrate theaberrations of the ocular optical system 10 of the first embodiment,which are the aberrations obtained based on the assumption that thereversely tracking of the ray direction is the parallel imaging rayspassing through the pupil 2 and the ocular optical system 10 in orderfrom the eye-side and focused on the display screen 100 for imaging. Inthe present embodiment, each aberration behavior shown in each of theaberrations can decide the corresponding aberration behavior for imagingof the imaging rays from the display screen 100 on the retina of the eyeof the observer. In other words, when each aberration behavior in eachof the aberrations is smaller, each aberration behavior for imaging onthe retina of the eye of the observer may also be smaller so the imagewith better imaging quality can be observed by the observer. FIG. 8Aillustrates the longitudinal spherical aberration when a pupil radiusthereof is 2 mm in the first embodiment. FIG. 8B and FIG. 8C illustratea field curvature aberration in a sagittal direction and a fieldcurvature aberration in a tangential direction on the display screen 100when wavelengths are 470 nm, 555 nm and 650 nm in the first embodiment.FIG. 8D illustrates a distortion aberration on the display screen 100when wavelengths are 470 nm, 555 nm and 650 nm in the first embodiment.In FIG. 8A which illustrates the longitudinal spherical aberration inthe first embodiment, the curve of each wavelength is close to oneanother and approaches the center position, which indicates that theoff-axis ray of each wavelength at different heights is concentratedaround the imaging point. The skew margin of the curve of eachwavelength indicates that the imaging point deviation of the off-axisray at different heights is controlled within a range of ±0.37 mm.Hence, it is evident that the spherical aberration of the samewavelength can be significantly improved according to the presentembodiment. In addition, the curves of the three representativewavelengths (red, green, and blue) are close to one another, whichindicates that the imaging positions of the rays with differentwavelengths are rather concentrated; therefore, the chromatic aberrationcan be significantly improved as well.

In FIG. 8B and FIG. 8C which illustrate two diagrams of field curvatureaberrations, the focal length variation of the three representativewavelengths within the entire field of view falls within the range of±3.5 mm, which indicates that aberration of the optical system providedin the first embodiment can be effectively eliminated. In FIG. 8D, thediagram of distortion aberration shows that the distortion aberration inthe first embodiment can be maintained within the range of ±18%, whichindicates that the distortion aberration in the first embodiment cancomply with the imaging quality requirement of the optical system.Accordingly, compared to the existing ocular optical system, the ocularoptical system provided in the first embodiment can have the favorableimaging quality, given that SL is shortened to about 62.198 mm. As aresult, according to the first embodiment, the length of the opticalsystem can be shortened and the apparent field of view can be enlargedwithout sacrificing the favorable optical properties. In this way, theproduct design with miniaturization, low aberration and large apparentfield of view taken into account can be realized.

FIG. 11 is a schematic view illustrating an ocular optical systemaccording to the second embodiment of the invention, and FIG. 12A toFIG. 12D illustrate a longitudinal spherical aberration and otheraberrations of the ocular optical system according to the secondembodiment of the invention. With reference to FIG. 11, the ocularoptical system 10 according to the second embodiment of the invention issimilar to that provided in the first embodiment, while the differencestherebetween are as follows. The optical data, the asphericcoefficients, and the parameters of the lens elements 3 and 4 in thesetwo embodiments are different to some extent. Further, in the presentembodiment, the eye-side surface 41 of the second lens element 4 is aconvex surface, and has a convex portion 411 in a vicinity of theoptical axis I and a convex portion 413 in a vicinity of a periphery ofthe second lens element 4. For clear illustration, it should bementioned that the same reference numbers of the concave portions andthe convex portions in the two embodiments are omitted from FIG. 11.

Detailed optical data of the ocular optical system 10 in the secondembodiment are indicated in FIG. 13. In the second embodiment, EFL ofthe ocular optical system 10 is 39.843 mm, ω thereof is 44.744°, TTLthereof is 46.202 mm, EPD thereof is 2.000 mm, 0.5 times DLD thereof is30.894 mm, and SL thereof is 61.243 mm.

The aspheric coefficients of the eye-side surfaces 31 and 41 and thedisplay-side surfaces 32 and 42 in the formula (1) are indicated in FIG.14 according to the second embodiment.

In addition, the relationship among the important parameters pertainingto the ocular optical system 10 in the second embodiment is indicated inFIG. 43.

In FIG. 12A which illustrates the longitudinal spherical aberration whenthe pupil radius is 2.0000 mm according to the second embodiment, theimaging point deviation of the off-axis ray at different heights iscontrolled within a range of ±0.35 mm. In FIG. 12B and FIG. 12C whichillustrate two diagrams of field curvature aberrations, the focal lengthvariation of the three representative wavelengths within the entirefield of view falls within the range of ±2.5 mm. In FIG. 12D, thediagram of distortion aberration shows that the distortion aberration inthe second embodiment can be maintained within the range of ±22%.Accordingly, compared to the first embodiment, the second embodiment canhave the favorable imaging quality, given that SL is shortened to about61.243 mm.

According to the above description, compared to the first embodiment,the advantages of the second embodiment are as follows. The systemlength SL in the second embodiment is shorter than the system length SLin the first embodiment; the longitudinal spherical aberration in thesecond embodiment is less than the longitudinal spherical aberration inthe first embodiment; and the field curvature in the second embodimentis less than the field curvature in the first embodiment.

FIG. 15 is a schematic view illustrating an ocular optical systemaccording to the third embodiment of the invention, and FIG. 16A to FIG.16D illustrate a longitudinal spherical aberration and other aberrationsof the ocular optical system according to the third embodiment of theinvention. With reference to FIG. 15, the ocular optical system 10according to the third embodiment of the invention is similar to thatprovided in the first embodiment, while the differences therebetween areas follows. The optical data, the aspheric coefficients, and theparameters of the lens elements 3 and 4 in these two embodiments aredifferent to some extent. Further, in the present embodiment, theeye-side surface 41 of the second lens element 4 has a concave portion412 in a vicinity of the optical axis I and a convex portion 413 in avicinity of a periphery of the second lens element 4. Further, in thepresent embodiment, the display-side surface 42 of the second lenselement 4 has a convex portion 421 in a vicinity of the optical axis Iand a concave portion 424 in a vicinity of a periphery of the secondlens element 4. For clear illustration, it should be mentioned that thesame reference numbers of the concave portions and the convex portionsin the two embodiments are omitted from FIG. 15.

Detailed optical data of the ocular optical system 10 in the thirdembodiment are indicated in FIG. 17. In the third embodiment, EFL of theocular optical system 10 is 31.996 mm, ω thereof is 50.209°, TTL thereofis 37.688 mm, EPD thereof is 2.000 mm, 0.5 times DLD thereof is 30.503mm, and SL thereof is 45.688 mm.

The aspheric coefficients of the eye-side surfaces 31 and 41 and thedisplay-side surfaces 32 and 42 in the formula (1) are indicated in FIG.18 according to the third embodiment.

In addition, the relationship among the important parameters pertainingto the ocular optical system 10 in the third embodiment is indicated inFIG. 43.

In FIG. 16A which illustrates the longitudinal spherical aberration whenthe pupil radius is 2.0000 mm according to the third embodiment, theimaging point deviation of the off-axis ray at different heights iscontrolled within a range of ±0.13 mm. In FIG. 16B and FIG. 16C whichillustrate two diagrams of field curvature aberrations, the focal lengthvariation of the three representative wavelengths within the entirefield of view falls within the range of ±0.35 mm. In FIG. 16D, thediagram of distortion aberration shows that the distortion aberration inthe third embodiment can be maintained within the range of ±20%.Accordingly, compared to the existing ocular optical system, the ocularoptical system provided in the third embodiment can have the favorableimaging quality, given that the system length SL is shortened to about45.688 mm.

According to the above description, compared to the first embodiment,the advantages of the third embodiment are as follows. The system lengthSL of the ocular optical system 10 in the third embodiment is less thanthe system length SL in the first embodiment; the half apparent field ofview ω in the third embodiment is greater than the half apparent fieldof view ω in the first embodiment; the longitudinal spherical aberrationin the third embodiment is less than the longitudinal sphericalaberration in the first embodiment; and the field curvature in the thirdembodiment is less than the field curvature in the first embodiment.Besides, because a thickness difference between portions in a vicinityof the optical axis and in a vicinity of a periphery of the lens elementin the fourth embodiment is less than that of the first embodiment, theocular optical system in the third embodiment is, in comparison withthat provided in the first embodiment, easier to be manufactured andthus has higher yield.

FIG. 19 is a schematic view illustrating an ocular optical systemaccording to the fourth embodiment of the invention, and FIG. 20A toFIG. 20D illustrate a longitudinal spherical aberration and otheraberrations of the ocular optical system according to the fourthembodiment of the invention. With reference to FIG. 19, the ocularoptical system 10 according to the fourth embodiment of the invention issimilar to that provided in the first embodiment, while differencestherebetween are as follows. The optical data, the asphericcoefficients, and the parameters of the lens elements 3 and 4 in thesetwo embodiments are different to some extent. Further, in the presentembodiment, the eye-side surface 41 of the second lens element 4 has aconcave portion 412 in a vicinity of the optical axis I and a convexportion 413 in a vicinity of a periphery of the second lens element 4.Furthermore, in the present embodiment, the display-side surface 42 ofthe second lens element 4 has a convex portion 421 in a vicinity of theoptical axis I and a concave portion 424 in a vicinity of a periphery ofthe second lens element 4. For clear illustration, it should bementioned that the same reference numbers of the concave portions andthe convex portions in the two embodiments are omitted from FIG. 19.

Detailed optical data of the ocular optical system 10 in the fourthembodiment are indicated in FIG. 21. In the fourth embodiment, EFL ofthe ocular optical system 10 is 33.001 mm, ω thereof is 50.030°, TTLthereof is 37.760 mm, EPD thereof is 2.000 mm, 0.5 times DLD thereof is30.550 mm, and SL thereof is 45.760 mm.

The aspheric coefficients of the eye-side surfaces 31 and 41 and thedisplay-side surfaces 32 and 42 in the formula (1) are indicated in FIG.22 according to the fourth embodiment.

In addition, the relationship among the important parameters pertainingto the ocular optical system 10 in the fourth embodiment is indicated inFIG. 43.

In FIG. 20A which illustrates the longitudinal spherical aberration whenthe pupil radius is 2.0000 mm according to the fourth embodiment, theimaging point deviation of the off-axis ray at different heights iscontrolled within a range of ±0.13 mm. In FIG. 20B and FIG. 20C whichillustrate two diagrams of field curvature aberrations, the focal lengthvariation of the three representative wavelengths within the entirefield of view falls within the range of ±0.55 mm. In FIG. 20D, thediagram of distortion aberration shows that the distortion aberration inthe fourth embodiment can be maintained within the range of ±25%.Accordingly, compared to the existing ocular optical system, the ocularoptical system provided in the fourth embodiment can have the favorableimaging quality, given that the system length SL is shortened to about45.760 mm.

According to the above description, compared to the first embodiment,the advantages of the fourth embodiment are as follows. The systemlength SL of the ocular optical system 10 in the fourth embodiment isless than the system length SL in the first embodiment; the halfapparent field of view ω in the fourth embodiment is greater than thehalf apparent field of view ω in the first embodiment; the sphericalaberration in the fourth embodiment is less than the sphericalaberration in the first embodiment; and the field curvature in thefourth embodiment is less than the field curvature in the firstembodiment. Besides, because a thickness difference between portions ina vicinity of the optical axis and in a vicinity of a periphery of thelens element in the fourth embodiment is less than that of the firstembodiment, the ocular optical system in the fourth embodiment is, incomparison with that provided in the first embodiment, easier to bemanufactured and thus has higher yield.

FIG. 23 is a schematic view illustrating an ocular optical systemaccording to the fifth embodiment of the invention, and FIG. 24A to FIG.24D illustrate a longitudinal spherical aberration and other aberrationsof the ocular optical system according to the fifth embodiment of theinvention. With reference to FIG. 23, the ocular optical system 10according to the fifth embodiment of the invention is similar to thatprovided in the first embodiment, while the differences are as follows.The optical data, the aspheric coefficients, and the parameters of thelens elements 3 and 4 in these two embodiments are different to someextent. Further, in the present embodiment, the eye-side surface 41 ofthe second lens element 4 is a convex surface, and has a convex portion411 in a vicinity of the optical axis I and a convex portion 413 in avicinity of a periphery of the second lens element 4. For clearillustration, it should be mentioned that the same reference numbers ofthe concave portions and the convex portions in the two embodiments areomitted from FIG. 23.

Detailed optical data of the ocular optical system 10 in the fifthembodiment are indicated in FIG. 25. In the fifth embodiment, EFL of theocular optical system 10 is 50.719 mm, ω thereof is 44.002°, TTL thereofis 59.009 mm, EPD thereof is 2.000 mm, 0.5 times DLD thereof is 54.899mm, and SL thereof is 75.146 mm.

The aspheric coefficients of the eye-side surfaces 31 and 41 and thedisplay-side surfaces 32 and 42 in the formula (1) are indicated in FIG.26 according to the fifth embodiment.

In addition, the relationship among the important parameters pertainingto the ocular optical system 10 in the fifth embodiment is indicated inFIG. 43.

In FIG. 24A which illustrates the longitudinal spherical aberration whenthe pupil radius is 2.0000 mm according to the fifth embodiment, theimaging point deviation of the off-axis ray at different heights iscontrolled within a range of ±0.65 mm. In FIG. 24B and FIG. 24C whichillustrate two diagrams of field curvature aberrations, the focal lengthvariation of the three representative wavelengths within the entirefield of view falls within the range of ±8 mm. In FIG. 24D, the diagramof distortion aberration shows that the distortion aberration in thefifth embodiment can be maintained within the range of ±3.5%.Accordingly, compared to the existing ocular optical system, the ocularoptical system provided in the fifth embodiment can have the favorableimaging quality, given that the system length SL is shortened to about75.146 mm.

According to the above description, compared to the first embodiment,the advantages of the fifth embodiment are as follows. The distortion ofthe fifth embodiment is less than the distortion of the firstembodiment. Besides, because a thickness difference between portions ina vicinity of the optical axis and in a vicinity of a periphery of thelens element in the fifth embodiment is less than that of the firstembodiment, the ocular optical system in the fifth embodiment is, incomparison with that provided in the first embodiment, easier to bemanufactured and thus has higher yield.

FIG. 27 is a schematic view illustrating an ocular optical systemaccording to the sixth embodiment of the invention, and FIG. 28A to FIG.28D illustrate a longitudinal spherical aberration and other aberrationsof the ocular optical system according to the sixth embodiment of theinvention. With reference to FIG. 27, the ocular optical system 10according to the sixth embodiment of the invention is similar to thatprovided in the first embodiment, while the differences therebetween areas follows. The optical data, the aspheric coefficients, and theparameters of the lens elements 3 and 4 in these two embodiments aredifferent to some extent. Further, in the present embodiment, theeye-side surface 41 of the second lens element 4 has a concave portion412 in a vicinity of the optical axis I and a convex portion 413 in avicinity of a periphery of the second lens element 4. Further, in thepresent embodiment, the display-side surface 42 of the second lenselement 4 has a convex portion 421 in a vicinity of the optical axis Iand a concave portion 424 in a vicinity of a periphery of the secondlens element 4. For clear illustration, it should be mentioned that thesame reference numbers of the concave portions and the convex portionsin the two embodiments are omitted from FIG. 27.

Detailed optical data of the ocular optical system 10 in the sixthembodiment are indicated in FIG. 29. In the sixth embodiment, EFL of theocular optical system 10 is 32.106 mm, ω thereof is 44.999°, TTL thereofis 37.451 mm, EPD thereof is 2.000 mm, 0.5 times DLD thereof is 30.550mm, and SL thereof is 45.451 mm.

The aspheric coefficients of the eye-side surfaces 31 and 41 and thedisplay-side surfaces 32 and 42 in the formula (1) are indicated in FIG.30 according to the sixth embodiment.

In addition, the relationship among the important parameters pertainingto the ocular optical system 10 in the sixth embodiment is indicated inFIG. 44.

In FIG. 28A which illustrates the longitudinal spherical aberration whenthe pupil radius is 2.0000 mm according to the sixth embodiment, theimaging point deviation of the off-axis ray at different heights iscontrolled within a range of ±0.13 mm. In FIG. 28B and FIG. 28C whichillustrate two diagrams of field curvature aberrations, the focal lengthvariation of the three representative wavelengths within the entirefield of view falls within the range of ±0.8 mm. In FIG. 28D, thediagram of distortion aberration shows that the distortion aberration inthe sixth embodiment can be maintained within the range of ±20%.Accordingly, compared to the existing ocular optical system, the ocularoptical system provided in the sixth embodiment can have the favorableimaging quality, given that the system length SL is shortened to about45.451 mm.

According to the above description, compared to the first embodiment,the advantages of the sixth embodiment are as follows. The system lengthSL in the sixth embodiment is less than the system length SL in thefirst embodiment; the longitudinal spherical aberration in the sixthembodiment is less than the longitudinal spherical aberration in thefirst embodiment; and the field curvature in the sixth embodiment isless than the field curvature in the first embodiment. Besides, becausea thickness difference between portions in a vicinity of the opticalaxis and in a vicinity of a periphery of the lens element in the sixthembodiment is less than that of the first embodiment, the ocular opticalsystem in the sixth embodiment is, in comparison with that provided inthe first embodiment, easier to be manufactured and thus has higheryield.

FIG. 31 is a schematic view illustrating an ocular optical systemaccording to the seventh embodiment of the invention, and FIG. 32A toFIG. 32D illustrate a longitudinal spherical aberration and otheraberrations of the ocular optical system according to the seventhembodiment of the invention. With reference to FIG. 31, the ocularoptical system 10 according to the seventh embodiment of the inventionis similar to that provided in the first embodiment, while thedifferences therebetween are as follows. The optical data, the asphericcoefficients, and the parameters of the lens elements 3 and 4 in thesetwo embodiments are different to some extent. For clear illustration, itshould be mentioned that the same reference numbers of the concaveportions and the convex portions in the two embodiments are omitted fromFIG. 31.

Detailed optical data of the ocular optical system 10 in the seventhembodiment are indicated in FIG. 33. In the seventh embodiment, EFL ofthe ocular optical system 10 is 44.000 mm, ω thereof is 44.999°, TTLthereof is 60.039 mm, EPD thereof is 2.000 mm, 0.5 times DLD thereof is38.440 mm, and SL thereof is 81.380 mm.

The aspheric coefficients of the eye-side surfaces 31 and 41 and thedisplay-side surfaces 32 and 42 in the formula (1) are indicated in FIG.34 according to the seventh embodiment.

In addition, the relationship among the important parameters pertainingto the ocular optical system 10 in the seventh embodiment is indicatedin FIG. 44.

In FIG. 32A which illustrates the longitudinal spherical aberration whenthe pupil radius is 2.0000 mm according to the seventh embodiment, theimaging point deviation of the off-axis ray at different heights iscontrolled within a range of ±7 mm. In FIG. 32B and FIG. 32C whichillustrate two diagrams of field curvature aberrations, the focal lengthvariation of the three representative wavelengths within the entirefield of view falls within the range of ±7 mm. In FIG. 32D, the diagramof distortion aberration shows that the distortion aberration in theseventh embodiment can be maintained within the range of ±16%.Accordingly, compared to the existing ocular optical system, the ocularoptical system provided in the seventh embodiment can have the favorableimaging quality, given that the system length SL is shortened to about81.380 mm.

According to the above description, compared to the first embodiment,the advantages of the seventh embodiment are as follows. The distortionaberration of the seventh embodiment is less than the distortionaberration of the first embodiment. Besides, because a thicknessdifference between portions in a vicinity of the optical axis and in avicinity of a periphery of the lens element in the seventh embodiment isless than that of the first embodiment, the ocular optical system in theseventh embodiment is, in comparison with that provided in the firstembodiment, easier to be manufactured and thus has higher yield.

FIG. 35 is a schematic view illustrating an ocular optical systemaccording to the eighth embodiment of the invention, and FIG. 36A toFIG. 36D illustrate a longitudinal spherical aberration and otheraberrations of the ocular optical system according to the eighthembodiment of the invention. With reference to FIG. 35, the ocularoptical system 10 according to the eighth embodiment of the invention issimilar to that provided in the first embodiment, while the differencestherebetween are as follows. The optical data, the asphericcoefficients, and the parameters of the lens elements 3 and 4 in thesetwo embodiments are different to some extent. Further, in the presentembodiment, the eye-side surface 41 of the second lens element 4 has aconcave portion 412 in a vicinity of the optical axis I and a concaveportion 414 in a vicinity of a periphery of the second lens element 4.For clear illustration, it should be mentioned that the same referencenumbers of the concave portions and the convex portions in the twoembodiments are omitted from FIG. 35.

Detailed optical data of the ocular optical system 10 in the eighthembodiment are indicated in FIG. 37. In the eighth embodiment, EFL ofthe ocular optical system 10 is 52.179 mm, ω thereof is 44.999°, TTLthereof is 61.242 mm, EPD thereof is 2.000 mm, 0.5 times DLD thereof is38.443 mm, and SL thereof is 82.054 mm.

The aspheric coefficients of the eye-side surfaces 31 and 41 and thedisplay-side surfaces 32 and 42 in the formula (1) are indicated in FIG.38 according to the eighth embodiment.

In addition, the relationship among the important parameters pertainingto the ocular optical system 10 in the eighth embodiment is indicated inFIG. 44.

In FIG. 36A which illustrates the longitudinal spherical aberration whenthe pupil radius is 2.0000 mm according to the eighth embodiment, theimaging point deviation of the off-axis ray at different heights iscontrolled within a range of ±2.4 mm. In FIG. 36B and FIG. 36C whichillustrate two diagrams of field curvature aberrations, the focal lengthvariation of the three representative wavelengths within the entirefield of view falls within the range of ±7 mm. In FIG. 36D, the diagramof distortion aberration shows that the distortion aberration in theeighth embodiment can be maintained within the range of ±30%.Accordingly, compared to the existing ocular optical system, the ocularoptical system provided in the eighth embodiment can have the favorableimaging quality, given that the system length SL is shortened to about82.054 mm.

FIG. 39 is a schematic view illustrating an ocular optical systemaccording to the ninth embodiment of the invention, and FIG. 40A to FIG.40D illustrate a longitudinal spherical aberration and other aberrationsof the ocular optical system according to the ninth embodiment of theinvention. With reference to FIG. 39, the ocular optical system 10according to the ninth embodiment of the invention is similar to thatprovided in the first embodiment, while the differences therebetween areas follows. The optical data, the aspheric coefficients, and theparameters of the lens elements 3 and 4 in these two embodiments aredifferent to some extent. For clear illustration, it should be mentionedthat the same reference numbers of the concave portions and the convexportions in the two embodiments are omitted from FIG. 39.

Detailed optical data of the ocular optical system 10 in the ninthembodiment are indicated in FIG. 41. In the ninth embodiment, EFL of theocular optical system 10 is 40.951 mm, ω thereof is 43.999°, TTL thereofis 47.042 mm, EPD thereof is 2.000 mm, 0.5 times DLD thereof is 29.763mm, and SL thereof is 64.004 mm.

The aspheric coefficients of the eye-side surfaces 31 and 41 and thedisplay-side surfaces 32 and 42 in the formula (1) are indicated in FIG.42 according to the ninth embodiment.

In addition, the relationship among the important parameters pertainingto the ocular optical system 10 in the ninth embodiment is indicated inFIG. 44.

In FIG. 40A which illustrates the longitudinal spherical aberration whenthe pupil radius is 2.0000 mm according to the ninth embodiment, theimaging point deviation of the off-axis ray at different heights iscontrolled within a range of ±0.4 mm. In FIG. 40B and FIG. 40C whichillustrate two diagrams of field curvature aberrations, the focal lengthvariation of the three representative wavelengths within the entirefield of view falls within the range of ±3.5 mm. In FIG. 40D, thediagram of distortion aberration shows that the distortion aberration inthe ninth embodiment can be maintained within the range of ±25%.Accordingly, compared to the existing ocular optical system, the ocularoptical system provided in the ninth embodiment can have the favorableimaging quality, given that the system length SL is shortened to about64.004 mm.

FIG. 43 and FIG. 44 are table diagrams showing the optical parametersprovided in the foregoing nine embodiments. If the relationship amongthe optical parameters in the ocular optical system 10 provided in theembodiments of the invention satisfies at least one of the followingconditions, the design of the ocular optical system with favorableoptical performance and the reduced length in whole becomes technicalfeasible:

1. If the system can satisfy the following condition, the aberrations ofthe first lens element 3 can be corrected by the second lens element 4without overly affecting the focal length and an image magnifying powerof the system: 1.5≤|f2/f1|. If the following condition can be furthersatisfied, the refracting power of the second lens element 4 can beprevented from insufficient for correcting the aberrations of the firstlens element 3: 1.5≤|f2/f1|≤8.

2. Because 250 mm is the least distance of distinct vision of youngpeople (the closest distance that the eye of young people is able toclearly focus on), the magnifying power of the system can approach aratio of 250 mm and EFL. Therefore, if the following condition can besatisfied, the magnifying power of the system is unlikely to be so largethat can increase the thickness and manufacturing difficulty of the lenselement: 250 mm/EFL≤10. If the following condition can be furthersatisfied, EFL is unlikely to be so long that can affect the systemlength: 3.5≤250 mm/EFL≤10.

3. If the following condition can be satisfied, the observer is unlikelyto experience the narrow vision: 40°≤ω. If the following condition canbe further satisfied, a designing difficulty is not increased:40°≤ω≤60°.

4. If the system can satisfy at least one of the following conditions:2.5≤T1/T2, 9≤T1/G12, 2≤T2/G12, 2≤G2D/T1, 20≤G2D/G12, G2D/T2≤16,2.2≤G2D/ALT and SL/T1≤7.6 (more preferably, at least one of thefollowing conditions is to be satisfied: 2.5≤T1/T2≤6, 9≤T1/G12≤20,2≤T2/G12≤4, 2≤G2D/T1≤5, 20≤G2D/G12≤62, 5≤G2D/T2≤16, 2.2≤G2D/ALT≤6 and1.9≤SL/T1≤7.6), the thickness and interval of each lens element can bemaintained at an appropriate value, so as to prevent the slimness of theocular optical system 10 in whole from being affected by any overlylarge parameter, or prevent the assembly from being affected or themanufacturing difficulty from increased by the any overly smallparameter.

5. If the system can satisfy at least one of the following conditions:2≤G2D/ER, ER/T1≤5.5, ER/T2≤8, ER/G12≤20, 1.5≤(0.5×DLD)/ER and 2≤EFL/ER(more preferably, at least one of the following conditions is to besatisfied: 2≤G2D/ER≤5.5, 1≤ER/T1≤5.5, 3≤ER/T2≤8, 9≤ER/G12≤20,1.5≤(0.5×DLD)/ER≤4.6 and 2≤EFL/ER≤6), the exit pupil distance and theoptical parameters of the lens elements can be maintained at anappropriate value, so as to prevent the slimness of the ocular opticalsystem 10 in whole from being affected by any overly large parameter, orprevent the assembly from being affected or the manufacturing difficultyfrom increased by the any overly small parameter.

6. If the system can satisfy the following conditions, the narrow visiondue to the half apparent field of view being too small can be preventedby restricting the relationship of the focal length and the size of thedisplay screen: EFL/(0.5×DLD)≤1.4. If the following condition can befurther satisfied, the half apparent field of view is unlikely to be solarge that can increase the designing difficulty: 0.3≤EFL/(0.5×DLD)≤1.4.

7. If the system can satisfy the condition of 1≤DLD/D2, by restrictingthe relationship of the size of the display screen 100 and the size ofthe second lens element 4, the system magnification is unlikely to be solarge that can increase the thickness and the manufacturing difficultyof the lens element. More preferably, 1≤DLD/D2≤2.2.

However, due to the unpredictability of the design of an optical system,with the framework set forth in the embodiments of the invention, theocular optical system satisfying said conditions can be characterized bythe reduced system length, the enlarged available aperture, theincreased apparent field of view, the improved imaging quality, or theimproved assembly yield, such that the shortcomings described in therelated art can be better prevented.

To sum up, the ocular optical system 10 described in the embodiments ofthe invention may have at least one of the following advantages and/orachieve at least one of the following effects.

1. The longitudinal spherical aberrations, field curvature aberrations,and distortion aberrations provided in the embodiments of the inventionall comply with usage specifications. Moreover, the off-axis rays withdifferent heights and the three representative wavelengths (470 nm, 555nm, and 650 nm), or the three representative wavelengths (430 nm, 530nm, and 620 nm) are all gathered around imaging points, and according toa deviation range of each curve, it can be observed that deviations ofthe imaging points of the off-axis rays with different heights are allcontrolled and thus capable of suppressing spherical aberrations, imageaberrations, and distortion. With reference to the imaging quality data,distances among the three representative wavelengths (470 nm, 555 nm,and 650 nm), or the three representative wavelengths (430 nm, 530 nm,and 620 nm) are fairly close, which indicates that rays with differentwavelengths in the embodiments of the invention can be well concentratedunder different circumstances to provide the capability of suppressingdispersion. As such, it can be known from the above that, theembodiments of the invention can provide favorable optical properties.

2. The eye-side surface 31 of the first lens element 3 provided hereinis characterized by having the convex portion 311 in a vicinity of theoptical axis I, which is conducive to concentration of rays. Thedisplay-side surface 32 of the first lens element 3 is characterized bythe Fresnel surface 33, which is conducive to the reduction in thethickness of the first lens element 3. The second lens element 4 ischaracterized by having negative refracting power, which is conducive tothe correction of image aberration generated by the first lens element3.

3. In addition, system limitations may be further added by using anycombination relation of the parameters selected from the providedembodiments to implement the system design with the same framework setforth in the embodiments of the invention. In view of theunpredictability of the design of an optical system, with the frameworkset forth in the embodiments of the invention, the ocular optical systemsatisfying said conditions can be characterized by the reduced systemlength, the enlarged exit pupil diameter, the improved imaging quality,or the improved assembly yield, such that the shortcomings described inthe related art can be better prevented.

4. The aforementioned limitation relations are provided in an exemplarysense and can be randomly and selectively combined and applied to theembodiments of the invention in different manners; the invention shouldnot be limited to the above examples. In implementation of theinvention, apart from the above-described relations, it is also possibleto add additional detailed structure such as more concave and convexcurvatures arrangement of a specific lens element or a plurality of lenselements so as to enhance control of system property and/or resolution.For example, it is optional to form an additional convex portion in thevicinity of the optical axis on the eye-side surface of the first lenselement. It should be noted that the above-described details can beoptionally combined and applied to the other embodiments of theinvention under the condition where they are not in conflict with oneanother.

It will be apparent to those skilled in the art that variousmodifications and variations can be made to the structure of the presentinvention without departing from the scope or spirit of the invention.In view of the foregoing, it is intended that the present inventioncover modifications and variations of this invention provided they fallwithin the scope of the following claims and their equivalents.

What is claimed is:
 1. An ocular optical system, for imaging of imagingrays entering an eye of an observer via the ocular optical system from adisplay screen, a side facing towards the eye being an eye-side, a sidefacing towards the display screen being a display-side, the ocularoptical system comprising a first lens element and a second lens elementfrom the eye-side to the display-side in order along an optical axis,the first lens element and the second lens element each comprising aneye-side surface and a display-side surface; the eye-side surface of thefirst lens element having a convex portion in a vicinity of a peripheryof the first lens element; the eye-side surface of the second lenselement having a convex portion in a vicinity of a periphery of thesecond lens element; and lens elements having refracting power of theocular optical system are only the first lens element and the secondlens element; wherein DLD is a diagonal length of the display screencorresponding to one single pupil of the observer, T1 is a thickness ofthe first lens element along the optical axis, ER is a distance from apupil of the eye of the observer to the first lens element along theoptical axis, G12 is an air gap from the first lens element to thesecond lens element along the optical axis, and the ocular opticalsystem satisfies the equation:2.652≤((0.5×DLD)+T1)/(ER+G12)≤4.517.
 2. The ocular optical systemaccording to claim 1, wherein T2 is a thickness of the second lenselement along the optical axis, and the optical imaging lens satisfiesthe equation:15.240≤(T1+G12+(0.5×DLD))/T2≤27.840.
 3. The ocular optical systemaccording to claim 1, wherein ALT is a sum of thicknesses of the firstlens element and the second lens element along the optical axis, D2 is adiameter of a clear aperture of the eye-side surface of the second lenselement, ω is one half the field of view of the observer, and the ocularoptical system satisfies the equations:0. 828 mm/°≤(ALT+D2)/ω<1.572 mm/°.
 4. The ocular optical systemaccording to claim 1, wherein SL is a distance from a pupil of the eyeof the observer to the display screen along the optical axis, T2 is athickness of the second lens element along the optical axis, and theocular optical system satisfies the equation:5.253≤((0.5×DLD)+SL)/(ER+T2)≤7.631.
 5. The ocular optical systemaccording to claim 1, wherein D1 is a diameter of a clear aperture ofthe eye-side surface of the first lens element, ω is one half the fieldof view of the observer, and the ocular optical system satisfies theequation:0.763 mm/°≤(D1+T1)ω≤1.539 mm/°.
 6. The ocular optical system accordingto claim 1, wherein G2D is a distance from the second lens element tothe display screen along the optical axis, T2 is a thickness of thesecond lens element along the optical axis, and the ocular opticalsystem satisfies the equations:1.865≤(G12+G2D)/(ER+T2)≤2.970.
 7. The ocular optical system according toclaim 1, wherein EFL is an effective focal length of the ocular opticalsystem, T2 is a thickness of the second lens element along the opticalaxis, and the ocular optical system satisfies the equation:2.271≤EFL/(ER−FT2)≤3.300.
 8. An ocular optical system, for imaging ofimaging rays entering an eye of an observer via the ocular opticalsystem from a display screen, a side facing towards the eye being aneye-side, a side facing towards the display screen being a display-side,the ocular optical system comprising a first lens element and a secondlens element from the eye-side to the display-side in order along anoptical axis, the first lens element and the second lens element eachcomprising an eye-side surface and a display-side surface; the eye-sidesurface of the first lens element having a convex portion in a vicinityof a periphery of the first lens element; the eye-side surface of thesecond lens element having a convex portion in a vicinity of a peripheryof the second lens element; and lens elements having refracting power ofthe ocular optical system are only the first lens element and the secondlens element; wherein DLD is a diagonal length of the display screencorresponding to one single pupil of the observer, T1 is a thickness ofthe first lens element along the optical axis, ER is a distance from apupil of the eye of the observer to the first lens element along theoptical axis, and the ocular optical system satisfies the equation:2.785≤((0.5×DLD)+T1)/ER≤4.800.
 9. The ocular optical system according toclaim 8, wherein G12 is an air gap from the first lens element to thesecond lens element along the optical axis, T2 is a thickness of thesecond lens element along the optical axis, and the optical imaging lenssatisfies the equation:15.240≤(T1+G12+(0.5×DLD))/T2≤27.840.
 10. The ocular optical systemaccording to claim 8, wherein ALT is a sum of thicknesses of the firstlens element and the second lens element along the optical axis, D2 is adiameter of a clear aperture of the eye-side surface of the second lenselement, ω is one half the field of view of the observer, and the ocularoptical system satisfies the equations:0.828 mm/°≤(ALT+D2)/ω≤1.572 mm/°.
 11. The ocular optical systemaccording to claim 8, wherein SL is a distance from a pupil of the eyeof the observer to the display screen along the optical axis, T2 is athickness of the second lens element along the optical axis, and theocular optical system satisfies the equation:5.253≤((0.5×DLD)+SL)/(ER+T2)≤7.631.
 12. The ocular optical systemaccording to claim 8, wherein D1 is a diameter of a clear aperture ofthe eye-side surface of the first lens element, ω is one half the fieldof view of the observer, and the ocular optical system satisfies theequation:0.763 mm/°≤(D1+T1)/ω≤1.539 mm/°.
 13. The ocular optical system accordingto claim 8, wherein G12 is an air gap from the first lens element to thesecond lens element along the optical axis, G2D is a distance from thesecond lens element to the display screen along the optical axis, T2 isa thickness of the second lens element along the optical axis, and theocular optical system satisfies the equations:1.865≤(G12+G2D)/(ER+T2)≥2.970.
 14. The ocular optical system accordingto claim 8, wherein EFL is an effective focal length of the ocularoptical system, T2 is a thickness of the second lens element along theoptical axis, and the ocular optical system satisfies the equation:2.271≤EFL/(ER−FT2)≤3.300.